A294626 a(n) = (1/(24*n)) * Sum_{d|n} A008683(n/d) * (A288877(d) - A288261(d)).

42, -3171, 515242, -88552695, 16361485098, -3146078130083, 622295456184618, -125653124401054383, 25774485201611434666, -5353054527354475135971, 1122995842490069166600618, -237552033781060445940477047, 50601782105864798623718932266

Offset: 1

Author

Seiichi Manyama, Feb 12 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..424

Crossrefs

Cf. A008683, A288261, A288877, A294974.

Programs

Mathematica

terms = 13;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
a[n_] := (1/(24 n))*Sum[MoebiusMu[n/d]*SeriesCoefficient[E4[x]/E2[x] - E6[x]/E4[x], {x, 0, d}], {d, Divisors[n]}];
Array[a, terms] (* Jean-François Alcover, Feb 26 2018 *)

Formula

a(n) ~ -(-1)^n * exp(Pi*sqrt(3)*n) / (8*n). - Vaclav Kotesovec, Jun 03 2018